There's no such rule or principle as "since is usually supposed to be followed by a past simple verb".
The only relevant principle here is that repeatedly using past perfect unnecessarily can often be perceived as clumsy and excessively verbose. There's nothing actually wrong with OP's example, provided it's in a context where the primary narrative reference time is later than both the arrival and subsequent observations of rule-breaking...
1: He wasn't surprised. Since he had arrived, he had seen the rule broken more than once.
Note that since there means after [some specified time] not because [of some specified fact]. Thus it's contextually obvious that he arrived before seeing the rules being broken, but his lack of surprise occurred after seeing that (at the "narrative time").
In such contexts it's perfectly natural for native speakers to dispense with the first use of past perfect, since (because! :) it's not really necessary (because since specifies the chronological sequence)...
2: He wasn't surprised. Since he arrived, he had seen the rule broken more than once.
In short, both versions are perfectly "grammatical", but many if not most native speakers wouldn't bother with the first instance of past perfect, for the sake of simplicity and clarity.